Question

find the length of the hypotenuse.

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs of the right - triangle. Here \(a = 48\) and \(b = 55\).

Step2: Calculate \(a^{2}+b^{2}\)

\(a^{2}=48^{2}=48\times48 = 2304\), \(b^{2}=55^{2}=55\times55 = 3025\). Then \(a^{2}+b^{2}=2304 + 3025=5329\).

Step3: Find the square - root

Since \(c^{2}=a^{2}+b^{2}=5329\), then \(c=\sqrt{5329}\). And \(\sqrt{5329}=73\).

Answer:

73